Modified Inertial Krasnosel'skii-Mann Type Method for Solving Fixed PointProblems in Real Uniformly Convex Banach Spaces
DOI:
https://doi.org/10.29020/nybg.ejpam.v17i3.5187Keywords:
Asymptotically Nonexpansive Mappings, Modified Inertial Krasnosel'skii-Mann, Continuous Mappings, Convergence, Fixed Points, Banach SpacesAbstract
We present an altered version of the inertial Krasnosel'skii-Mann algorithm and demonstrate convergence outcomes for mappings that are asymptotically nonexpansive within real, uniformly convex Banach spaces. To achieve our results, we skillfully construct the inequality in equation \eqref{6} and apply it accordingly. Our findings support and broadly generalize a number of significant findings from the literature. We demonstrate, as an application, the generation of maximal monotone operators' zeros via fixed point methods in Hilbert spaces. Additionally, we solve convex minimization issues using our fixed-point techniques.
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